The aim of the present numerical investigation is to explore the impact of magnetic field on peristaltic flow of an incompressible tangent-hyperbolic fluid in an asymmetric channel. The present physical model is developed based on the considered flow configuration and with the help of small Reynolds number approximations. The current flow problem is revealed under the influence of applied magnetic field. The asymmetric channel has been considered to narrate the present physical problem. Considered physical situation in the current investigation gives the unsteady coupled highly nonlinear system of partial differential equations. Also, the simplified equations for pressure, pressure gradient, and streamlines have been obtained with the help of suitable transformations. A regular perturbation scheme is employed to produce the semi-analytical results of the present problem. The influence of various physical parameters on pressure, pressure gradient, and streamlines are illustrated with the help of graphs. From the present analysis, it is observed that the increasing magnetic number decreases the pressure and pressure gradient in the channel. Also, the size of trapping bolus increases with increasing values of Weissenberg number. K E Y W O R D S asymmetric channel, magnetic field, peristaltic flow, Reynolds number 1 | INTRODUCTION Peristaltic flow of physiological fluids is a type of wave-frame movement existing inside the tube-shaped structures, which induces the motion of a particle/medium. Peristaltic transport mechanism is very important in many industrial and real-life applications. For instance, blood flow in the heart, lungs and dialysis works on the principles of peristaltic process. Also, other mechanisms include the peristaltic flow examples, such as movement of urine to bladder through kidney, motion of chyme in intestinal path, spermatozoa motion, movement of food in esophagus, vasomotion of arterioles, capillaries, and venules, and many other biomedical applications. However, in realistic view, the process such as sanitary fluid movement, corrosive fluids transfer, motion of toxic fluids in various industries, plasma flow, blood flow, alloys and liquid metals flow, heavy oil lubrication with greases, and many others will fail to follow the Newtonian flow conditions. However, for these types of practical applications, it is quite obvious to choose the non-Newtonian fluid flow behavior to determine the transport properties. Further, various researchers have considered and studied the different non-Newtonian fluids based on their practical applications and flow complexity. The theoretical and experimental study of peristaltic fluid flow in a pump was studied by Latham. 1 It is clearly observed from Latham's study that the variations in the velocity profile were useful to describe how viscosity causes the peristaltic pump to work. Also, forward and backward flow occurs even though there is no pressure across the pump. Further, Latham's study was continued by Jaffrin and Shapiro 2 and they described the influ...

Objectives:The study intends to investigate the problem of peristalsis transport of hyperbolic tangent fluid in a tapered asymmetric channel. Methods: The two-dimensional equations of a hyperbolic tangent fluid have been simplified under the suspicions of low Reynolds number and long wavelength approximations. The reduced equations are solved by using standard perturbation technique. The numerical results obtained are presented in the graphical form for various values of physical parameters and are discussed. Findings: It is showing that for the larger values of non-uniform parameter, pressure rise diminishes and the axial velocity diminishes at the core part of the channel and increases at the right and left side of the channel for the increasing values of non-uniform parameter. Applications: Hyperbolic tangent fluid model anticipate the shear thinning phenomenon very accurately and are being used mostly in laboratory experiments and industries.

The present physical problem has a significant number of applications in intra-uterine fluid motion with tiny particles in a nonpregnant uterus, and this situation of fluid motion is very important in examining the embryo motion in a uterus. Due to these real-life applications, in the current investigation, a perturbation-oriented numerical investigation has been performed to describe the characteristics features of velocity, pressure rise, and trapping bolus through streamlines in a tapered channel under a porous medium. The present physical model results in the governing two-dimensional coupled nonlinear flow equations under low Reynolds number and long-wavelength approximations. A suitable equation for stream function is derived and a regular perturbation scheme is employed to produce the numerical solutions in terms of pressure rise, velocity, and streamlines for various values of physical parameters. The current investigation depicts that the enhancing Darcy parameter upsurged the pressure field, and the increasing power-law index suppressed the pressure field in the flow regime. The rincreasing channel width significantly diminished the velocity field at the central portion of the channel. The size of the trapping bolus suppressed for the enhancing values of Weissenberg number. In addition, the size of the trapping bolus increased for the magnifying values of wave amplitudes. Finally, current numerical solutions reasonably agree with the previously published results in the literature, and this fact confirms the accuracy of the present problem.

We have considered the peristaltic mechanism of incompressible viscous hyperbolic tangent fluid with the impact of uniform magnetic field. The tapered asymmetric channel is assumed to be designed due to a peristaltic wave train on the non uniform walls taking different amplitudes and phase. This model anticipates the shear thinning phenomenon very precisely and are being used frequently in laboratory experiments and industries. Here we consider the Reynolds number to be small enough and wavelength for simplification of two dimensional equations of a hyperbolic tangent fluid. The non-linear governing equations for the tangent hyperbolic fluid are solved by utilising Regular perturbation methodology. The exact solutions for the pressure gradient and pressure rise are determined analytically. Its behaviour is discussed computationally with reference to different physical parameters.

The study explores to analyze the problem of peristaltic mechanism of tangent hyperbolic fluid through porous medium in an asymmetric channel. The two-dimensional peristaltic flow of hyperbolic tangent fluid in an asymmetric channel through porous medium is analyzed under the long wavelength and low Reynolds number assumptions. The flow is investigated in a wave frame of reference moving with velocity of the wave. The perturbation series is used to obtain the solution for stream function, pressure gradient and pressure rise. The results were studied for different values of the physical parameters of the problem and illustrated graphically. It is observed that pressure rise diminishes for the larger values of Darcy number. Pressure gradient decreases for increment in Darcy number. Hyperbolic tangent fluid model anticipates the shear thinning phenomenon very accurately and are being used mostly in laboratory experiments and industries.